Given the large volume of technical documents available, it is crucial to automatically organize and categorize these documents to be able to understand and extract value from them. Towards this end, we introduce a new research problem called Facet Extraction. Given a collection of technical documents, the goal of Facet Extraction is to automatically label each document with a set of concepts for the key facets (e.g., application, technique, evaluation metrics, and dataset) that people may be interested in. Facet Extraction has numerous applications, including document summarization, literature search, patent search and business intelligence. The major challenge in performing Facet Extraction arises from multiple sources: concept extraction, concept to facet matching, and facet disambiguation. To tackle these challenges, we develop FacetGist, a framework for facet extraction. Facet Extraction involves constructing a graph-based heterogeneous network to capture information available across multiple local sentence-level features, as well as global context features. We then formulate a joint optimization problem, and propose an efficient algorithm for graph-based label propagation to estimate the facet of each concept mention. Experimental results on technical corpora from two domains demonstrate that Facet Extraction can lead to an improvement of over 25% in both precision and recall over competing schemes.